Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#127 | C2 | semidirect |
| 2. C2×C5×#214 | C2 | semidirect |
| 3. C2×C5×#213 | C2 | semidirect |
| 4. C5×#875 | C2 | semidirect |
| 5. C5×#803 | C2 | semidirect |
| 16. #5074 | C5 | direct (N × H) |
| 19. C5×#127 | D3 | semidirect |
| 32. C5×C3⋊C8 | D4 | semidirect |
| 33. C3×#127 | C2×C5 | semidirect |
| 34. C2×#214 | C2×C5 | semidirect |
| 35. C2×#213 | C2×C5 | semidirect |
| 36. #875 | C2×C5 | semidirect |
| 37. #803 | C2×C5 | semidirect |
| 78. #127 | C5×D3 | semidirect |
| 95. C3⋊C8 | C5×D4 | semidirect |
| 113. C3×C5 | #496 | semidirect |
| 141. C5 | #5074 | direct (N × H) |
| 150. C3 | C5×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#127 | 2 |
| C2×C5×#214 | 2 |
| C2×C5×#213 | 2 |
| C5×#875 | 2 |
| C5×#803 | 2 |
| C5×#496 | 3 |
| #5074 | 5 |